Tauwehe
\left(x-5\right)\left(x-2\right)\left(x+2\right)\left(x+5\right)
Aromātai
x^{4}-29x^{2}+100
Graph
Tohaina
Kua tāruatia ki te papatopenga
x^{4}-29x^{2}+100=0
Kia tauwehea ai te kīanga, me whakaoti te whārite ina ōrite ki te 0.
±100,±50,±25,±20,±10,±5,±4,±2,±1
Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau 100, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.
x=2
Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.
x^{3}+2x^{2}-25x-50=0
Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{4}-29x^{2}+100 ki te x-2, kia riro ko x^{3}+2x^{2}-25x-50. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.
±50,±25,±10,±5,±2,±1
Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau -50, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.
x=-2
Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.
x^{2}-25=0
Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}+2x^{2}-25x-50 ki te x+2, kia riro ko x^{2}-25. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.
x=\frac{0±\sqrt{0^{2}-4\times 1\left(-25\right)}}{2}
Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 1 mō te a, te 0 mō te b, me te -25 mō te c i te ture pūrua.
x=\frac{0±10}{2}
Mahia ngā tātaitai.
x=-5 x=5
Whakaotia te whārite x^{2}-25=0 ina he tōrunga te ±, ina he tōraro te ±.
\left(x-5\right)\left(x-2\right)\left(x+2\right)\left(x+5\right)
Me tuhi anō te kīanga whakatauwehe mā ngā pūtake i riro.
Ngā Tauira
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Ngā Tepe
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